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4. Let P be any point on the ellipse E: x² + 25 1. 9 (i) Show that the equation of the tangent at P = (5 cos 0, 3 sin ) is 3x cos 0 + 5y sin 0 = 15. π. (ii) Assume that 0 <0 < . The tangent at the vertex A = (5,0) on the major axis meets the tangent at P at the point R. If O is the origin, show that OR is parallel to A'P where A' = (-5,0) the opposite vertex to A.

4. Let P be any point on the ellipse E: x² + 25 1. 9 (i) Show that the equation of the tangent at P = (5 cos 0, 3 sin ) is 3x cos 0 + 5y sin 0 = 15. π. (ii) Assume that 0 <0 < . The tangent at the vertex A = (5,0) on the major axis meets the tangent at P at the point R. If O is the origin, show that OR is parallel to A'P where A' = (-5,0) the opposite vertex to A.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 22RE
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4. Let P be any point on the ellipse E: x² + 25 9 = 1. (i) Show that the equation of the tangent at P = (5 cos 0, 3 sin 0) is 3x cos 0 + 5y sin = 15. (ii) Assume that 0 <0 < . The tangent at the vertex A = (5,0) on the major axis meets the tangent at P at the point R. If O is the origin, show that OR is parallel to A'P where A' = (-5, 0) the opposite vertex to A.
Transcribed Image Text:4. Let P be any point on the ellipse E: x² + 25 9 = 1. (i) Show that the equation of the tangent at P = (5 cos 0, 3 sin 0) is 3x cos 0 + 5y sin = 15. (ii) Assume that 0 <0 < . The tangent at the vertex A = (5,0) on the major axis meets the tangent at P at the point R. If O is the origin, show that OR is parallel to A'P where A' = (-5, 0) the opposite vertex to A.
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